Nonlinearity is inherent in most systems confronting scientific endeavors, and presents particular challenges to a wide array of scientific fields. The behavior of a nonlinear system is often described by a nonlinear system of equations. A nonlinear system of equations is a set of simultaneous equations, in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it (them). Because nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations (linearization).
A nonlinear system of equations, or nonlinearity, applies to nonlinear digital pre- or post-distortion schemes of nonlinear components or nonlinear systems with memory, such as power amplifiers for wireless-, wireline-, or optical-fiber-communication. Primary problems caused by system components exhibiting dynamic nonlinearity (i.e. nonlinear behavior with memory) are out-of-band emissions and in-band distortion, which lead to design problems such as low energy efficiency and degraded performance. Non-linear pre- or post-distortion schemes or combinations thereof attempt to mitigate the unwanted effects resulting from out-of-band emissions and in-band distortion by attempting to modify (pre- or post-distorting) input or output signals of nonlinear systems.
Interference cancellation can be a key enabler of full-duplex radio communication. One particular type of interference is known as ‘self-interference,’ which refers to interference from the one signal pathway on to another. Self-interference cancellation can enable lower cost components to be integrated in a transceiver, for example, by relaxing the requirements on expensive duplexers, thereby saving billions of dollars in mass produced transceivers for FDD and full-duplex radios. Self-interference cancellation techniques that are implemented in the digital domain can potentially cancel up to 20-25 dB of interference.